BUENOS AIRES—U.S. Treasury Secretary Steven Mnuchin said he “wouldn’t minimize” the possibility that the U.S. will impose tariffs on all $500 billion worth of goods that the U.S. imports from China, amplifying a threat President Donald Trump made in a television interview earlier in the week.

Mr. Mnuchin was speaking ahead of a meeting among G-20 finance ministers and central bankers here.

Mr. Mnuchin stressed that the administration’s goal is to achieve a “more balanced” trade relationship with China, by getting the Asian country to open its economy and permitting U.S. exports there to increase.

The Treasury secretary pointed out several sectors where U.S. sales to China could rise, including energy, agricultural products and technology.

“China has a large, growing population that will consume more products” and that likes American products, he said, while cautioning that U.S. companies shouldn’t be pressured to share their technology.

Mr. Mnuchin also talked about the administration’s willingness to sign trade agreements with the European Union and Japan, always with the objective of opening up markets and permitting what he called “real” free trade.

“If Europe believes in free trade, we’re ready to sign a free-trade agreement,” he said, adding that any agreement would have to eliminate tariffs, along with other barriers and subsidies. “It has to be all three issues,” he said.

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During the meeting with reporters Saturday, the Treasury secretary played down comments Mr. Trump made earlier in the week about the Federal Reserve and currency markets. Mr. Trump said in a tweet and in a television interview he wasn’t happy that the Fed is raising short-term interest rates, which he said is undermining administration efforts to rev up U.S. economic growth. It was unusual because the White House usually refrains from commenting on monetary policy.

Mr. Mnuchin said he and the president still “fully” supported Fed independence. He also said the U.S. isn’t trying to interfere in foreign-exchange markets after Mr. Trump accused China and the European Union of manipulating their currencies to make their economies more competitive.

The president has threatened tariffs on $500 billion in Chinese imports before. On July 6 on Air Force One, the president told reporters tariffs could eventually hit $550 billion in imports from China.

When asked during Friday’s CNBC interview, “Will you ever get to 500, though?” Mr. Trump responded that he is “ready to go to 500,” referring to the approximate dollar value of Chinese goods exported to the U.S. last year.

“I’m doing this to do the right thing for our country. We have been ripped off by China for a long time,” he said.

Earlier this month, the U.S. imposed levies on $34 billion of Chinese exports of machinery, components and electronics. Also scheduled are tariffs on $16 billion of Chinese electronics and other components.

The U.S. has identified a further $200 billion in Chinese goods the U.S. may target for tariffs, for a total of $250 billion. Anything further, Mr. Trump has said, depends on the extent to which China retaliates.